age vs old age

age and old age both are nouns.

Word	Noun	Adjective	Verb	Adverb
age	Yes	No	Yes	No
old age	Yes	No	No	No

As nouns, age and old age are synonyms defined as:

Other synonyms of age include eld, geezerhood, years.

age (noun)	old age (noun)
how long something has existed	a late time of life
a time of life (usually defined in years) at which some particular qualification or power arises
a late time of life
an era of history having some distinctive feature
a prolonged period of time